X-ray driven and intrinsic dynamics in protein gels

We use X-ray photon correlation spectroscopy to investigate how structure and dynamics of egg white protein gels are affected by X-ray dose and dose rate. We find that both, changes in structure and beam-induced dynamics, depend on the viscoelastic properties of the gels with soft gels prepared at low temperatures being more sensitive to beam-induced effects. Soft gels can be fluidized by X-ray doses of a few kGy with a crossover from stress relaxation dynamics (Kohlrausch–Williams–Watts exponents \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \approx 1.5$$\end{document}k≈1.5 to 2) to typical dynamical heterogeneous behavior (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k<$$\end{document}k<1) while the high temperature egg white gels are radiation-stable up to doses of 15 kGy with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\ge 1.5$$\end{document}k≥1.5. For all gel samples we observe a crossover from equilibrium dynamics to beam induced motion upon increasing X-ray fluence and determine the resulting fluence threshold values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _D$$\end{document}ΦD. Surprisingly small threshold values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _D=(3 \pm 2)\times 10^{-3} \,\textrm{ph}\,$$\end{document}ΦD=(3±2)×10-3ph s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1 nm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-2}$$\end{document}-2 can drive the dynamics in the soft gels while for stronger gels this threshold is increased to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _D=(0.9 \pm 0.3) \,\textrm{ph}$$\end{document}ΦD=(0.9±0.3)ph s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1 nm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-2}$$\end{document}-2. We explain our observations with the viscoelastic properties of the materials and can connect the threshold dose for structural beam damage with the dynamic properties of beam-induced motion. Our results suggest that soft viscoelastic materials can display pronounced X-ray driven motion even for low X-ray fluences. This induced motion is not detectable by static scattering as it appears at dose values well below the static damage threshold. We show that intrinsic sample dynamics can be separated from X-ray driven motion by measuring the fluence dependence of the dynamical properties.


Results
Measurement scheme and data collection. The experiments were performed at the coherence applications beamline P10 of PETRA III (DESY). The hen egg white was filled into quartz capillaries of diameter 1.5 mm and samples were heated to temperatures in the range 50-85 • C, which covers the denaturation temperatures of the different protein components in the egg white 45,50 . After heating for 40 min the samples were left at room temperature for about 1 h. The XPCS measurements were performed in the USAXS (ultra-small angle X-ray scattering) setup with a distance of 21.2 m between the sample holder and the Eiger X 4M detector (75 × 75 µm 2 pixel size) that records time series of the scattered intensity (Fig. 1). A photon energy of 8.54 keV ( = 1.45 Å) was used. The range of wave vector transfers q of 0.005-0.2 nm −1 gives access to the dynamics on the length scale of the gel's mesh size 51 . The photon fluence is controlled by inserting absorbers with different thickness before the sample (see "Methods").
Static ultra small angle X-ray scattering. We access the structural changes in the egg white gel caused by radiation effects via temporal changes in the scattered intensity. Figure 2 displays the time and dose resolved azimuthally integrated X-ray scattering intensity for egg white samples prepared at 63 • C (Fig. 2a) and 78 • C (Fig. 2b). The series depicted in the panel figures were recorded with a dose rate of 4 kGy s −1 reaching a maximum accumulated dose of 800 kGy. We observe significant X-ray-induced changes to the gel structure for both samples with the structure of the low temperature sample (Fig. 2a) being more sensitive to dose than the high temperature sample (Fig. 2b). Intensity curves for other temperatures and dose rates are presented in Fig. S3 in the SI. The effects of the accumulated dose on the structure are shown in the insets of Fig. 2 by plotting relative changes to the intensity ( I(t)/I 0 (t = 0) ) averaged in the q-interval from 0.006 to 0.03nm −1 . The data points obtained from Fig. 2a,b (in dark blue) can be compared to other measurements performed with smaller dose rates that are shown in different colors as indicated by the colorbar above the inset.
The effects of the dose rate on the structure are shown in the insets of Fig. 2 by plotting relative changes to the intensity ( I(t)/I 0 (t = 0) ) averaged in the q-interval from 0.006 to 0.03 nm −1 . This interval covers the region of the most apparent changes to I(q) and is identical to the range of q-values available for the XPCS analysis of the dynamics.
The plots reveal that the structure of the low temperature egg white sample ( T prep = 63 • C, Fig. 2a) starts to degrade after a dose of a few kGy visible via a strong increase in the relative intensity. We define the threshold value for radiation induced structural changes via the dose value at which the relative changes in scattering intensity exceed 1%, similar to Reiser et al. 24 . These threshold dose values as indicated by vertical lines in the inset of Fig. 2a are in the range of 3-9 kGy and nearly independent of the applied dose rate. Upon accumulating further dose the scattered intensity reaches a maximum before it starts to decrease. The position and the value of this maximum depend on the applied dose rate with higher dose rates leading to a more pronounced maximum at higher dose values. The other samples prepared at 63-70 • C show a similar trend (see SI material).
A different behavior is observed for the samples prepared at temperature of 73 • C and above (Fig. 2b). Here, a decrease in scattered intensity becomes evident only at higher dose values of 15-150 kGy without notable increase in intensity in-between. Moreover, the threshold values of dose induced changes depend on the dose rate. Applying high dose rates results in radiation induced changes appearing at higher dose values which we will discuss later in view of the sample dynamics. www.nature.com/scientificreports/ We attribute the observed overall differences in radiation susceptibility of both egg white samples to the different content of denaturated proteins. Hen egg white consists of approximately 40 different proteins 45,50,52,53 among which ovalbumin (54%) [54][55][56][57] and ovotransferrin (12%) 58,59 represent the largest fractions. The denaturation temperature of ovotransferrin is in the range of 61-69 • C 45,50,60 while ovalbumin typically denaturates at temperatures slightly above 70 • C 46,61 . In addition to the higher volume fraction of denaturated proteins above 70 • C, ovalbumin forms a stronger gel network than ovotransferrin due to the exposure of its sulfhydryl groups [45][46][47] . Subsequently, all egg white samples prepared at temperatures T prep ≥ 73 • C display a reduced susceptibility to radiation damage (see SI material). In contrast, the higher radiation sensitivity of the 63 • C egg white sample is representative for all samples in the temperature range 63-70 • C which form the weakly linked gel network of denaturated ovotransferrin. As a consequence of the findings in this analysis and for reasons of simplicity, we will refer to the samples prepared at 63-70 • C as soft gel networks and to the samples prepared at 73-85 • C as strong gel networks. X-ray photon correlation spectroscopy. To understand the processes involved we need to resolve also the dynamic processes that accompany the absorption of ionizing radiation. For this we make use of the high coherence of the synchrotron facility PETRA III and perform XPCS experiments to evaluate the influence of X-ray irradiation on the dynamics via two-time correlation functions (TTCs).
Illuminating a disordered egg white sample with a coherent X-ray beam produces a speckle pattern 62-64 that fluctuates according to the microscopic motion of the protein gel. We correlate these fluctuating intensities I(q, t) at time t 1 and t 2 in a TTC to obtain information on the dynamics 37,65 : Here, . . . p represents the average over all detector pixels within an annulus of average momentum transfer q. Figure 3a shows an example of a TTC obtained from an egg white gel prepared at 63 • C and measured with a dose rate of 0.09 kGy s −1 . The TTC decays with increasing distance from the diagonal ( t 1 = t 2 ) which represents the increasing decorrelation of the speckle patterns due to the sample dynamics. We also observe a decreasing width of the correlation function with increasing measurement time indicating a radiation induced speed-up of the dynamics caused by the accumulated dose.
To quantify this dose effect we extract g (2) (q, τ ) intensity autocorrelation functions via horizontal cuts starting from the diagonal of the TTC at different times t 2 and define τ = t 1 − t 2 with t 1 ≥ t 2 . The dose equivalents of these starting times depend on the photon fluence via D ∝ t 2 · and serve here as dose labels for the g (2) functions, noting that the dose increases further with progressing t 1 for each point of the correlation function. The correlation functions are modeled by a Kohlrausch-Williams-Watts (KWW) function 66 : where β(q) is the q-dependent speckle contrast 67 ( β(q = 0.02 nm −1 ) ≈ 9.7% ), Ŵ(q) is the decay rate and k is the KWW exponent containing information about the type of motion 33,43 . Figure 3b shows g (2) functions and corresponding KWW fits from the TTC in Fig. 3a. We observe that for the 63 • C sample the resulting decay rates Ŵ (Fig. 3b inset) increase rapidly after an accumulation of a few kGy (inset of Fig. 3b). Figure 3c displays the q-dependence of the g (2) functions at an identical starting dose of 1 kGy. The corresponding decay rates (Fig. 3c, inset) reveal a linear dependence Ŵ = v · q with v denoting a velocity. Together with the observed values of the KWW exponents ≥ 1.5 (lower left inset in Fig. 3c) this type of ballistic motion is typical for gels and connected with stress relaxation after gel formation 51,68-72 . We will later use this fluence-and sample-dependent velocity to compare fluence effects independent of the wave vector transfer q.
Dose effects on dynamics. We apply this XPCS analysis procedure to all samples in the temperature range 63-85 • C that we measured with ten different dose rates in the range from 0.002 to 4 kGy s −1 , which are the same measurements as in the analysis of the static scattering above. The resulting values of the decay rates Ŵ as a function of dose and dose rate are displayed in Fig. 4 for four different preparation temperatures, noting that all measurements have been performed at room temperature. We observe a similar behavior in the dynamics as seen in the structural changes with the soft gel network samples (Fig. 4a,b) being more susceptible to dose effects than the ones forming a strong gel network (Fig. 4c,d).
In the temperature range 63-70 • C the decay rates are almost constant until a dose of few kGy. Crossing this threshold dose value, the relaxation rate strongly increases by almost two orders of magnitude implying a fluidization of the soft gels formed by the heat denaturated ovotransferrin. This fluidization is accompanied by a decrease of KWW exponents to values k < 1 (insets in Fig. 4). The reverse is usually observed during the aging of a gel, i.e. rates decrease and KWW exponents increase until stress relaxation is the final mechanism of dynamics 73 . At the same time we observe a transition from ballistic ( Ŵ ∝ q ) to diffusive motion ( Ŵ ∝ q 2 ). Thus, the data suggests that the gel structure is fluidized under the influence of the radiation and becomes mobile again. This also explains the increase in the static scattering signal (inset of Fig. 2a) at doses D of 10-50 kGy as the fluidized gel is capable of further aggregation.
Beyond a dose of 10 kGy the decay rate reaches a dose rate-independent maximum value. This maximum is followed by a slow-down of the dynamics of one order of magnitude which starts around ≈ 50 kGy to the highest recorded doses of ≈ 600 kGy. This decrease sets in at lower doses for higher dose rates. The slow down is accompanied by an increase of the KWW exponents back to values of k ≈ 1.5 indicating that stress relaxation www.nature.com/scientificreports/ is re-established as the main relaxation mechanism for very high doses. This points towards a radiation induced denaturation of the remaining protein content, mostly ovalbumin, with the subsequent formation of a gel. A different picture emerges for the samples with a strong network (Fig. 4c,d) that have been prepared at temperatures of 73 • C and above. Here, the influence of the accumulated dose on the dynamics is much less pronounced. A maximum speed-up of the decay rate Ŵ by a factor of five becomes visible for T prep = 73 • C ( Fig. 4c) for the highest dose rates of 4 kGy s −1 and doses between 10 and 100 kGy. The KWW exponents vary only slightly (insets of Fig. 4c,d) indicating that the dynamics are always stress driven relaxation.
Generally speaking, our results demonstrate that the strong protein gels formed at higher temperatures are also dynamically much more stable under irradiation. Soft protein gels show dose induced fluidization for low doses followed by a slow-down due to radiation induced denaturation with further gel formation.
Dose rate effects and beam-induced dynamics. We investigate the nature of dose rate effects on the dynamics by continuously illuminating a single spot on an egg white sample while changing absorbers during the scan thus changing the dose rates. Examples of resulting TTCs are shown in Fig. 5 where scans with high dose rates of 4 kGy s −1 and 2 kGy s −1 are enclosed by scans with a smaller dose rate of 0.002 kGy s −1 . It can be seen that the almost frozen-in slow dynamics of the 80 • C-sample measured at the low dose rate is instantly accelerated when applying the higher dose rate but returns also instantly back to the slow dynamics as soon as the dose rate is decreased again. On top of this dose rate induced switching of the dynamics we observe a slower dose induced speed-up of the overall dynamics when comparing the first and the last TTC in Fig. 5 in agreement with the results from Fig. 4d.
Such flux dependent dynamics have been observed before in XPCS experiments on oxide and network glasses [26][27][28][29] , albeit with orders of magnitude higher dose rates, and also recently in dense protein glasses 30 . In our case the dynamics of the protein gels are governed by stress relaxations in which the correlation functions can be modeled as a series of consecutive relaxation events in the stressed material 68,74 . These relaxation events occur with a rate γ and an average displacement step of size δ . With this the g (2) function can be modeled as a sum over displacement events g (2) 2 ) for the decorrelation after N events, with typical displacement δ after a single relaxation event, yields the right values for the KWW parameter and the ballistic type of motion Ŵ ∝ q observed in our experiment. From the measured KWW exponents we infer values of qδ ≈ 0.01 to 0.1 (see SI). At these conditions the resulting relaxation rate of the correlation function is connected to the microscopic stress relaxation events via Ŵ ≈ γ qδ (see also SI), implying that the typical decorrelation rate Ŵ of the g (2) functions is a factor of 10-100 times smaller than the microscopic stress relaxation rate γ.
To disentangle dose and dose rate effects we evaluate the dynamics as a function of photon fluence for a fixed starting dose value of 1 kGy. Furthermore, we eliminate the q-dependence of the relaxation rates by making use of the ballistic type of motion with Ŵ = v · q which allows to extract the velocity v as a q-independent indicator of the sample dynamics (see also Fig. 3c). The increase of sample velocity as a function of the incident X-ray fluence is shown in Fig. 6a for the soft gel networks and in Fig. 6b for the strong gel networks, respectively.
We describe our data with a simple phenomenological model (see e.g. 30 ) in which v 0 represents the equilibrium sample velocity, is the X-ray fluence and α is a material constant describing the strength of the X-ray-matter interaction which accelerates the sample dynamics. This simple model describes the data reasonably well and the resulting fit parameters α and v 0 are shown in the insets of Fig. 6 (see SI for details of fit procedures). This linear dependence of the dynamics on photon fluence has been observed in other systems as well 26,[28][29][30] . It implies that the photon fluence induces an additional stress relaxation mechanism with the rate of microscopic events γ being proportional to the applied fluence via γ = α · �/δ. We define threshold values for the X-ray fluence D via the point where the induced dynamics, α� D outperform the intrinsic dynamics v 0 implying a beam-induced speed up of the dynamics by 100% . Averaging over all networks of a each type, we find fluence thresholds of (0.003 ± 0.002) ph s −1 nm −2 for the soft gel networks and (0.9 ± 0.3) ph s −1 nm −2 for the strong gels (indicated by vertical green sections in Fig. 6). The gel network prepared at 73 • C is excluded from this average due to the larger value of v 0 indicating that the network is in an intermediate state between strong to soft gel network.

Discussion
It is instructive to convert the velocities from Fig. 6 back into decay times of the correlation functions and to calculate the dose equivalents of these decay times. By this approach we consider that the sample accumulates further dose during the measurement of the correlation functions (increasing t 1 ). We choose the momentum transfers in line with the ones used in the analysis of the dose effects, that are q = 0.006 nm −1 for soft gel networks and q = 0.02 nm −1 for strong gel networks. We obtain the respective decay times via t ′ 1 = 1/(qv) using the velocities at a starting dose of 1 kGy from Fig. 6a,b. Multiplying these decay times t ′ 1 by the different dose rates D (see "Methods" section) yields the corresponding dose values D decay at which the correlation functions decay to a value of g (2) (t ′ 1 ) = 1 + β exp(−2) (Fig. 6c,d). We observe that D decay approaches constant values at fluences � > � D , indicated by the green lines. Above these fluences the g (2) function is entirely decorrelated by beam induced motion. Adding to D decay the dose value of 1 kGy already received at the start of the correlation yields threshold dose values beyond which all motion is beam-induced. www.nature.com/scientificreports/ For the soft gel networks, these maximum doses (i.e. the value where D decay levels off with increasing fluence in Fig. 6c,d are between 1.7 and 3 kGy, slightly below the thresholds values found from the analysis of the structural changes. In contrast, the strong gels can be fully decorrelated only at high X-ray fluences with dose values reaching 70-300 kGy. Interestingly, the structural analysis of the strong gels revealed thresholds for structural changes as low as 20 kGy (at dose rates of 0.3 kGy s −1 ) implying that in the fluence regime of fully beam induced motion the structural changes in the strong gels can occur already during the decorrelation of the correlation function.
In the next step, we estimate radical formation rates from the fluence thresholds D that we deduced from the fitting parameters α and v 0 . We assume that the absorption properties of the protein gels are comparable to the ones of water. In aqueous solutions, the radiolysis products are the main driver for beam damage and an absorption of a 100 eV photon energy results typically in 3 OH radicals 13 . In the irradiated sample volume of a soft gel network, � D = (0.003 ± 0.002) ph s −1 nm −2 causes a radical formation rate of ≈ 4 × 10 −7 radicals s −1 nm −2 or one radical per second per cube with an edge length of 138 nm. For a strong gel with � D = (0.9 ± 0.3) ph s −1 nm −2 , the same procedure yields a radical formation rate of ≈ 1.1 × 10 −4 radicals s −1 nm −3 or one radical per second per cube with an edge length of 20 nm. The estimates for the radical formation rate in the cuboid example volume yield surprisingly small density rates of radicals required to drive the dynamics instantaneously as it is observed in Fig. 5. This can best be understood considering the open gel network structure of the gels and the nature of the stress driven relaxation which requires to induce only a local breakage of a bond leading then to a coherent elastic response of the network 75 . Thus the few radicals do not move the whole corresponding volume, but rather trigger elastic relaxation events. The length scales found here agree with the reported values of spatial extension of decorrelation events in egg white 51 .
More quantitative insights are obtained when plotting the relative changes I/I 0 of the scattered intensities not as a function of dose, but as a function of exposure time t multiplied by the dose and dose-rate dependent relaxation rate Ŵ(D, �) (Fig. 7). The factor t · Ŵ(D, �) represents via g (2) (t) = 1 + β exp(−t · Ŵ(D, �)) the degree of correlation during the exposure time t. We observe that the relative intensity deviations are falling almost onto a single master curve (see also SI material) indicating that the damage thresholds of structural changes and the respective sample dynamics are connected. We observe that the soft gel networks all display a similar value of t · Ŵ(D, �) ≈ 1 at a 1% change to their relative scattering intensity, while for the strong gels this value is smaller with t · Ŵ(D, �) ≈ 0.1 . With Ŵ ≈ qδγ and values of qδ ≈ 0.01 to 0.1 we conclude that for the soft gels changes to the structure appear after t · γ = 10-100 stress events while for strong gels this is reduced to 1-10 events which is due to the very high doses applied during the very slow relaxation.
The maximum tolerable dose D max , the dose rate D and the dynamics are thus related via D max ∝ D / Ŵ(D, �) and it is instructive to examine this relationship for two limiting cases. In the first case, we assume that the relaxation rate Ŵ is independent of dose and dose rate ( Ŵ = Ŵ 0 ) which yields a limit D max ∝ D / Ŵ 0 favoring high dose rates and slow dynamics for achieving high damage thresholds. This is the regime in which, for example, a high X-ray fluence allows to run out radiation damage 24 . In the other limit we assume that the dynamics is beam induced motion only i.e. Ŵ = α · q · � leading to D max ∝ 1/αq which is then independent of dose rate. For the egg white gels Ŵ depends on both dose and dose rate and thus D max as well which explains the data shown in the inset of Fig. 2.
Finally, we can compare our results of α to published work on protein glasses 30 from which we extract values of α ≈ 2 × 10 −2 nm 3 ph −1 and to oxide glasses 26 which gives α ≈ 5 × 10 −6 nm 3 ph −1 (see Fig. 8). These values are four respectively eight orders of magnitude smaller than the corresponding α for hen-egg white at T prep = 63 • C. We attribute these large differences and the temperature dependent behavior of α observed in our study to the large differences in viscoelastic properties of the respective materials. Indeed, the relationship α ∝ γ · δ/� suggests that materials displaying slow dynamics and small values of elastic displacements δ will show accordingly small values of α . This in turn explains the generally enhanced values of α for softer materials. Rheology measurements of Bonilla and Clausen 76 revealed a sudden increase in yield stress of cooked egg white when the temperature exceeds 72 • C. This observation is in good agreement with our observation of soft and strong gels in terms of radiation susceptibility. Clearly, more systematic data on other sample systems and additional work by theory and simulation is needed to fully understand the relationship between sample properties and susceptibility to X-rays, in terms of both induced motion and beam damage.
In summary, our experimental results reveal a rich and complex dynamic response of protein gels to X-ray radiation. The combination of static and dynamic measurements shows that X-ray dose can lead to fluidized faster gels but also to more strongly bonded gels with slower dynamics. We find threshold values of X-ray fluence beyond which the dynamics of the protein gels are driven by X-ray induced stress relaxation. We infer that the susceptibility for X-ray driven motion depends on the viscoelastic properties of the sample. These results are important for experiments using synchrotron radiation and aiming to study kinetic and dynamic phenomena in viscoelastic materials which requires to match experimental time scales to sample time scales. Our findings demonstrate that the X-ray fluence is a key parameter for switching between dynamics driven by the X-ray beam and equilibrium dynamics of the sample.
Importantly, we identify values of dose rates and dose values at which the XPCS signal is reflecting true equilibrium dynamics for protein gels. Our study demonstrates that experimental setups and synchrotron instrumentation which want to make use of the high brilliance of 4th generation light sources need to be able reduce the photon density as effectively as possible. This requires making use of the enlarged coherence lengths of the new sources and perform experiments with large beams. The development of fast X-ray detectors with small pixel sizes and the use of increased sample-detector distances are needed to resolve the small speckles from large X-ray beams.      The flux was further reduced by sets of silicon absorbers with absorber n being equal to the thickness of a n × 25 µ m silicon wafer. The experimental absorption unit is realized as combinations of absorbers of different thicknesses allowing only for certain values of n (see Table 1). The reduced flux for absorber n is calculated from the X-ray transmission of a single 25 µ m wafer (73%) via:  where t exp is the exposure time and F red is the flux calculated from Eq. (4). E represents the energy of a single X-ray photon, in this case 8.54 keV, and T is the transmission of the sample with sample volume V. ρ is the mass density of a water equivalent (1000 kg m −3 ). The transmission T of 1.5 mm water for 8.54 keV X-rays is 27.8 %.
The dose rate D is derived from the accumulated dose via division by the exposure time t exp and is given in units of kGy s −1 : The fluences for the absorber configurations used and the resulting dose rates are given in Table 1.
(4) F n red. = F 0 · (0.73) n . Figure 8. Comparison to other sample systems. Parameter α describing the X-ray-induced acceleration of the dynamics for different sample systems (see Eq. (3)). The plot also includes data from Chushkin et al. 30 on protein glasses (yellow), Ruta et al. 26 on oxide glasses (grey) and Bin et al. 79 who investigated hydrated lysozyme (pink, see SI material for details).